First let me tell you all that i love the bitcoin concept. I wont detail the reasons as others have already did this numerous times, however i have a little concern.

How is the transaction chain gonna scale if at times the whole earth use it ?

It would becomes really hard to have and store the chain, and as well, could become hard to "keep up" for the network if transactions are created faster than it happens. I know, seems hard, however i work in finance and see daily algorithm doing like 1 million orders daily, making huge logs and huge database of which only a fraction of information is finally kept.

What are the technical solution that can be implemented to counter this eventual problem ?

First let me tell you all that i love the bitcoin concept. I wont detail the reasons as others have already did this numerous times, however i have a little concern.

How is the transaction chain gonna scale if at times the whole earth use it ?

It would becomes really hard to have and store the chain, and as well, could become hard to "keep up" for the network if transactions are created faster than it happens. I know, seems hard, however i work in finance and see daily algorithm doing like 1 million orders daily, making huge logs and huge database of which only a fraction of information is finally kept.

What are the technical solution that can be implemented to counter this eventual problem ?

Short story: Not everyone will keep the whole thing. Some will keep none, some headers only.

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Also keep in mind that as the number of transactions go up, the transaction fee reward from solving blocks will also go up.

To take the example used in the wiki article mentioned above: say the network was handling 2,000 transactions per second. This would be costing at least some people a lot in bandwidth. However, assuming a block takes ten minutes to solve, then there would be 2000 * 60 * 10 = 1,200,000 transactions in it. If the average transaction fee is 0.01, then that would be a 12,000 BTC reward for solving the block. That's ~$70,000 at today's exchange rates.

Also keep in mind that as the number of transactions go up, the transaction fee reward from solving blocks will also go up.

To take the example used in the wiki article mentioned above: say the network was handling 2,000 transactions per second. This would be costing at least some people a lot in bandwidth. However, assuming a block takes ten minutes to solve, then there would be 2000 * 60 * 10 = 1,200,000 transactions in it. If the average transaction fee is 0.01, then that would be a 12,000 BTC reward for solving the block. That's ~$70,000 at today's exchange rates.

The fee is going to drop by orders of magnitude soon imo.

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